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Complex curves in hypercomplex nilmanifolds with H-solvable Lie algebras
Journal of Geometry and Physics. 2023. Vol. 192. Article 104900.
Yulia Gorginyan
An operator I on a real Lie algebra is called a complex structure operator if and the -eigenspace is a Lie subalgebra in the complexification of . A hypercomplex structure on a Lie algebra is a triple of complex structures and K on satisfying the quaternionic relations. We call a hypercomplex nilpotent Lie algebra -solvable if there exists a sequence of -invariant subalgebrassuch that . We give examples of -solvable hypercomplex structures on a nilpotent Lie algebra and conjecture that all hypercomplex structures on nilpotent Lie algebras are -solvable. Let be a compact hypercomplex nilmanifold associated to an -solvable hypercomplex Lie algebra. We prove that, for a general complex structure L induced by quaternions, there are no complex curves in a complex manifold .
Publication based on the results of:
Chemical Papers 2026
Benzenoid hydrocarbons are structurally regular aromatic compounds, which makes them well suited for quantitative structure–property relationship (QSPR) studies. This study presents a QSPR analysis of nineteen benzenoid hydrocarbon species using degree-based topological co-indices. We developed a Python program to compute eleven degree-based topological co-indices from molecular graphs and evaluated their ability to explain variations in ...
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Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
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Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
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Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
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Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
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Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
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Added: August 31, 2026
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We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
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Added: August 31, 2026
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Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
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Lopatkin V., Kaygorodov I., Zhang Z., Journal of Geometry and Physics 2023 No. 187 P. 1–20
Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It is proven that all principal Galilean Lie algebras do not have non-trivial 12-derivations and as it follows they do not admit non-trivial transposed Poisson structures. Also, we proved that each complex finite-dimensional solvable Lie algebra admits a non-trivial transposed Poisson structure and a non-trivial Hom-Lie structure. ...
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Feigin B. L., Russian Mathematical Surveys 2017 Vol. 72 No. 4 P. 707–763
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Васильев М., Zabrodin A., Zotov A., Nuclear Physics B - Proceedings Supplements 2020 Vol. 952 No. 114931 P. 1–20
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Feigin E., Kato S., Makedonskyi I., Journal fuer die reine und angewandte Mathematik 2020 Vol. 764 P. 181–216
We study the non-symmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters are equal to the non-symmetric Macdonald polynomials specialized at infinity. Second, we show that these modules are isomorphic to the dual spaces of sections of certain sheaves on ...
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Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. ...
Added: March 10, 2020